In [1]} the authors consider expressibility of languages (and relations) by word equations and show that a language is expressible by \(\operatorname{WE}\)  if and only if it is expressible by a single word equation. The authors of [1]} also show that, for \(\Sigma \supseteq \lbrace a,b,c\rbrace \) , the regular language \(\lbrace a,b\rbrace ^*\)  is not expressible by a single word equation, and thus not in \(\operatorname{WE}\) . The same holds for the language \(\lbrace a^nb^n \mid n \in \mathbb {N}_0\rbrace \) . Since these languages are clearly expressible in \(\operatorname{WE}+ \operatorname{REG}\)  and \(\operatorname{WE}+ \operatorname{LEN}\)  respectively, we may immediately conclude the following.
